We derive an It^o's-type formula for the one dimensional stochastic heat equation driven by a space-time white noise. The proof is based on elementary properties of the S-transform and on the explicit representation of the solution process. We also discuss the relationship with other versions of this It^o formula existing in literature.
LANCONELLI A (2007). White noise approach to the Itˆo formula for the stochastic heat equation. COMMUNICATIONS ON STOCHASTIC ANALYSIS, 1(2), 311-320.
White noise approach to the Itˆo formula for the stochastic heat equation
LANCONELLI A
Investigation
2007
Abstract
We derive an It^o's-type formula for the one dimensional stochastic heat equation driven by a space-time white noise. The proof is based on elementary properties of the S-transform and on the explicit representation of the solution process. We also discuss the relationship with other versions of this It^o formula existing in literature.File in questo prodotto:
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